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We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

Data analysis and interpretation often relies on an approximation of an empirical dataset by some analytic functions or models. Actual implementations usually rely on a non-linear multi-dimensional optimization algorithm, typically…

This article discusses the problem of estimation of parameters in finite mixtures when the mixture components are assumed to be symmetric and to come from the same location family. We refer to these mixtures as semi-parametric because no…

This article explains an optimization-based approach for counting and localizing stars within a small cluster, based on photon counts in a focal plane array. The array need not be arranged in any particular way, and relatively small numbers…

We investigate the unsupervised node classification problem on random hypergraphs under the non-uniform Hypergraph Stochastic Block Model (HSBM) with two equal-sized communities. In this model, edges appear independently with probabilities…

Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…

We propose a Kronecker product model for correlation or covariance matrices in the large dimensional case. The number of parameters of the model increases logarithmically with the dimension of the matrix. We propose a minimum distance (MD)…

We present a method to estimate distances to stars with spectroscopically derived stellar parameters. The technique is a Bayesian approach with likelihood estimated via comparison of measured parameters to a grid of stellar isochrones, and…

Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift…

In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to…

In this paper some new properties and computational tools for finding KL-optimum designs are provided. KL-optimality is a general criterion useful to select the best experimental conditions to discriminate between statistical models. A…

The irregularities of a distribution of $N$ points in the unit interval are often measured with various notions of discrepancy. The discrepancy function can be defined with respect to intervals of the form $[0,t)\subset [0,1)$ or arbitrary…

We study the probabilistic existence of point configurations satisfying the $(0, m, d)$-net property in base $b$ within a randomly generated point set of size $N$ in the $d$-dimensional unit cube. We first derive an upper bound on the…

We give an explicit construction of two-dimensional point sets whose $L_p$ discrepancy is of best possible order for all $1\le p\le \infty$. It is provided by folding Hammersley point sets in base $b$ by means of the $b$-adic baker's…

On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the…

We study the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed,…

The accurate automated classification of variable stars into their respective sub-types is difficult. Machine learning based solutions often fall foul of the imbalanced learning problem, which causes poor generalisation performance in…

We obtain bounds on the stability of various self-gravitating astrophysical objects using a new measure of shape complexity known as configurational entropy. We apply the method to Newtonian polytropes, neutron stars with an…

Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…